Question: $J$ $K$ $L$ If: $ JK = 6x + 5$, $ KL = 2x + 6$, and $ JL = 35$, Find $KL$.
Answer: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {6x + 5} + {2x + 6} = {35}$ Combine like terms: $ 8x + 11 = {35}$ Subtract $11$ from both sides: $ 8x = 24$ Divide both sides by $8$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $KL$ $ KL = 2({3}) + 6$ Simplify: $ {KL = 6 + 6}$ Simplify to find ${KL}$ : $ {KL = 12}$